Marcus P. Corrosion mechanisms in theory and practice

Подождите немного. Документ загружается.

As illustrated in this chapter, Eq. (6), in parallel with the double-layer

capacitance C

, generates identifiable shapes on the impedance curves in the Bode

or Nyquist plane making possible to determine the number of chemical entities C

and C

participating in the reaction mechanism and thus providing information on the

reaction pattern. In terms of dissolution-passivation processes, capacitive responses

and negative resistances are related to inhibition or passivation whereas inductive

behaviors arise from catalytic effects or activating intermediates [4–8]. Acquisition

and processing of the transient response of electrochemical systems are easily

performed by modern laboratory equipment [5,6,49] and do not deserve special

attention in this chapter.

Local Electrochemical Measurements Practically any real-life solid electrode

exhibits, for structural and/or geometric reasons, heterogeneities in surface properties

and therefore in reactivity. The characteristic dimension may range between the

nanometric scale and the macroscopic size of the electrode. The traditional

electrochemical measurements provide surface average quantities, in both current

and potential. The information can be extremely biased, in somes cases totally

obscured, when sharp differences in reactivity are present. This is often the case for

anodic dissolution under the influence of metallurgy and/or composition. In order to

overcome the problem, techniques have been introduced for collecting local values

of the potential and current densities at short distances above the electrode surface.

Potential probes have long been known for attenuating the ohmic drop (Haber-

Luggin capillaries). Current probes have been developped intensively in the last 15

years. They are based on the measurements of the ohmic drop along a short current

path in the solution. Most of the studies used the so-called SVET technology

(scanning vibrating electrode technique) or to a lesser extent twin electrodes.

Current mapping thus obtained, with a spatial resolution at best about 15 μm, is

essentially applied for imaging galvanic currents associated with local cells in

corrosion. The techniques were extended to transient regimes, and spatially resolved

impedance measurements (LEIS, local electrochemical impedance spectroscopy)

[50–54] are now available with valuable performance. Undoubtedly, serious

advances in the interpretation of the kinetics of anodic dissolution can be expected

in the near future from the growing application of these techniques.

Complex transmittances relevant to corrosion phenomena have been introduced

[36,38,39]. Examples are given in several parts of the chapter. Two of them deserve

a particular interest. The case of techniques pertaining to the rotating ring disk

electrode (RRDE) is dealt with here. Electrogravimetric transmittance, a frequency-

resolved technique based on the electrochemical quartz crystal microbalance

(EQCM), was presented in a paper in 1996 [55].

Background of Time/Frequency-Resolved Measurements with an

Upstream (Emitter)–Downstream (Collector) Electrode Setup

These techniques are based on the discrimination between the dissolution and the

surface film growth component of the working electrode current [56]. The following

derivation makes used of the RRDE parameters indexed D (disk) and R (ring). The

transposition to an upstream-downstream pair of electrodes in any kind of flow

cell (e.g., channel flow double electrode, CFDE) is straightforward.

106 Keddam

Electrical Charge Balance In the non-steady-state regime the electrical charge

balance equation at the disk surface is

Anodic Dissolution 107

with I

= the electrical current supplied to the disk (at the exclusion of the

double-layer charging)

= the dissolution valence of the disk metal

= the flux of n

-valent cations released in the solution

= the faradic charge stored in surface layers

Equation (7) can be extended to the emission of more than one species with

different oxidation states: n

, m

,…

The Collection Efficiencies A fraction of the flux Φ

is collected and converted

into an electrochemical current I

on a downstream electrode owing to the transfer

of nR electrons in a convenient redox reaction. At steady state, the dimensionless

ratio

called the collection efficiency is determined entirely by the electrode layout. At the

non–steady state, Φ

is obtained:

In the time domain, through a deconvolution because one has

where N(t) is the characteristic transient collection efficiency of the device

experimentally defined for Φ

(t) = Dirac function δ(t). Unlike N, it depends

on both the electrode layout and the hydrodynamic parameters (fluid velocity,

viscosity, diffusivity).

In the frequency domain, through a simple division by the complex collection

efficiency N(

), which yields

The collection efficiencies are most easily determined by calibration experiments

on redox systems. In practice, the deconvolution of (10) is carried out by FFT

(fast Fourier transform) using the classical equation N(

) = Fourier transform

of N(t) and

Emission Efficiency and True Capacitance Exploitation in the time domain

of the differential (7) or of the integrated form Q

= n

+ Q

, where P

is the

amount of species generated by the disk dissolution, yields as the main information

the charge Q

involved in the surface layer. In the frequency domain, if Δ stands

for small-amplitude variables, (7) becomes

108 Keddam

where the ratio N

= (n

FΔΦ

) / (ΔI

) = 1 – (j

ΔQ

)/(

) is the emission efficien-

cy of the disk, a complex dimensionless quantity representing the fraction of the

disk current actually consumed in dissolution. Graphs of N

in the complex plane

provide a direct criterion about the kinetic role of the surface charge Q

. For instance

(ΔQ

) / (ΔI

) < 0; i.e., charge buildup producing a decrease of the dissolution cur-

rent (e.g., an electrochemically grown passivating layer) is displayed as a positive

imaginary part.

In order to get the true electrode capacitance Γ

, related exclusively to the film

growth, Eq. (14) can be further coprocessed with the faradic impedance of the disk:

The application of the technique in the time and frequency domains is illustrated

hereafter for the passivation of iron in acidic solutions.

Anodic Dissolution of Metals and Inductive Behaviors

It has long been recognized, originally in the time domain (transient measurements)

and later in the frequency domain (impedance measurements), that the non-

steady-state response of anodically dissolving metals displays in most cases an

inductive-like behavior. With the galvanostatic step used in the early work, this

behavior showed up as a voltage peak (overshoot), its counterpart in potentiostatic

mode being a minimum of current density. In the frequency domain an inductive

loop of the Nyquist plot was first identified by Keddam et al. [43–46] in the case

of iron in acidic media and interpreted by the so-called consecutive dissolution

mechanism (see later).

Classical Interpretation It was known from the previous work by Gerischer

and Mehl [42] on hydrogen evolution that a reaction path involving two consecutive

steps coupled by an adsorbed intermediate species can generate either an inductive

or a capacitive reaction impedance depending on the kinetic parameters. The

detailed derivation is given in the next section devoted to iron dissolution. It can

be shown according to (6) that, for a Langmuir type of adsorption and single-electron

transfers, Z

is given by the equation

where R

and ρ are resistances depending on the kinetic parameters of the reaction

steps, β is the maximum surface concentration of the adsorbed intermediate, J

and

are the current densities of the first and second steps, and F is the Faraday con-

stant. Z

is inductive for parameter values such that ρ is positive; this is shown to

occur for J

< J

. In this case Z

can be split immediately into two parallel

branches by identification of (15) to (16):

Anodic Dissolution 109

the self-inductance L being given by

The characteristic frequencies associated are in the admittance plane

and in the impedance plane

Both quantities are increasing functions of the DC current density:

The ratio Fβ is about one monolayer of elementary electrical charges per area unit

of the interface. Many experiments were found to agree with this model even

though several authors mentioned values definitely exceeding one monolayer and

serious deviations from Eqs. (18)–(20). Inductive loops at lower frequencies with

little or no current dependence are ignored in this discussion.

Weak Points and New Model: This problem was revisited in two papers

[57,58]. The first one established from a thorough survey of the literature of metal

and semiconductor dissolution that the frequency of the inductive impedance, in

contradiction of Eq. (19), is remarkably proportional to the DC current over several

orders of magnitude:

The meaning of the deviation between (19) and (21) can be perceived by noting

that according to (18) the frequency is determined by the faster of the two reaction

steps wherever (21) relates it to the slower one. In the second paper, an original

interpretation is proposed. It is based as well on a two-step process between the

metal atom at the lattice surface and the cation in solution on the outer side of the

double layer. A detailed presentation of this approach is far beyond the scope of

this chapter. It will be only outlined briefly. Basically, the relaxation is ascribed to

the time dependence of the surface concentration of an intermediate state of

dissolution. In that sense, the model ingredients are quite similar to those of the

consecutive mechanism, namely:

The ionization proceeds through a two-step path involving an intermediate state

(partially solvated).

The interface is (statistically) shared between the intermediate state (fractional

coverage θ) and the ground metallic state (1 – θ).

The model is still compatible with monovalent dissolution (Ag ⇒ Ag

, for

instance).

The time dependence is due to the difference between the fluxes of metal species

crossing the interface on the inner and outer sides of the intermediate state.

The new ideas lie essentially in the adjustement of the potential profiles in

the metal side (jellium) and the electrolyte side of the double layer in order to comply

with charge balance in conduction and electrostatic properties at the interface. This

is sketched in Figure 2. According to Ref. [58], the impedance has a structure similar

to (15). It can be cast in the form

110 Keddam

where C

and C

are the capacitances of the inner and outer parts of the double

layer, respectively. With this model, the linear dependence of frequency on DC

current can be simulated for acceptable sets of parameters including values of C

and

consistent with modern theories of the double layer. However, the ratio of one

monolayer is hardly obtained.

Actually, the model introduces a strong coupling between charge transfer and

double-layer structure, a feature generally discarded in spite of the high interfacial

concentration of cations released by the dissolution. In some way it may be regarded

as a ζ-potential approach to the problem. The topic of the kinetics content of the

inductive impedance of anodically dissolving metals is still an open question.

Obviously, it deserves further theoretical and experimental efforts.

ANODIC DISSOLUTION OF PURE METALS

Even though of little interest for practical corrosion problems, pure metals are

extremely basic to any approach to the mechanism of anodic dissolution, which is

believed to be much simpler than for alloys. However, the electrochemical behaviors

of high-purity metals can be deeply influenced by vanishingly amounts of impurities

able to segregate at the interface during anodic dissolution and also by metallurgical

factors. This may explain misleading interpretations and serious discrepancies

between materials from different sources with the same purity grade.

Mechanism of Heterogeneous Reaction:

Dissolution in the Active State

The case of iron will be taken as an example of heterogeneous reaction in the

active range of dissolution. Some other metals are also dealt with briefly.

Active Dissolution of Iron in Acidic Solutions

The active dissolution of iron in acidic media has been the subject of a very large

number of papers for the last 40 years. All the reaction mechanisms are based on the

generally agreed upon experimental evidence that the dissolution rate increases with

the solution pH at potentials well below the onset of passivity processes. The

apparently unacceptable participation of hydroxyl ions in the reaction at these low pH

Anodic Dissolution 111

Figure 2. (a) Sketch of the two consecutive ion-tranfer steps in anodic dissolution (b)

Sketch of the distribution of the interfacial potential drop Δ

across the electrochemical

double layer. From ref [58].

values can be related to the strong dissociative power of transition metals with

respect to water, an assumption supported for Fe by experimental evidence in

ultra-high vacuum [59]. Both groups of mechanisms stem from a common initial

hydrolysis step assumed to be at equilibrium:

112 Keddam

thus accounting for the pH dependence of the subsequent dissolution step. They

diverge from each other by the nature of the dissolution steps leading to the soluble

divalent species.

According to the catalytic mechanism [22], (FeOH)

ads

enters in a catalytic

sequence of dissolution at the end of which (FeOH)

ads

is regenerated and Fe

dissolved as (FeOH

A reluctant criticism of the catalytic mechanism is directed against the quantum

mechanically unacceptable transfer of two electrons in a single step. It must be

pointed out that on considering even a very crude atomistic content of this two-

electron step it appears less definitely excluded. Interpretation in terms of kink Fe

shifted to the next neighboring atom, denoted Fe′, in the dissolving edge:

clearly shows that the two electrons are not transferred from the same Fe species.

According to the consecutive mechanism [23], (FeOH)

ads

enters in a

noncatalytic one-electron transfer step by which it is oxidized to (FeOH

Finally, FeOH

is assumed to react with solution protons:

Mechanistic Criteria Based on Steady-State and Transient Polarization Data

For a long time, with the exception of the pioneering impedance approach of

Epelboin and Keddam [60], the controversy about the validity of these mechanisms

remained based on kinetic criteria drawn from true steady-state and fast polarization

techniques. Tafel slopes and orders of reaction with respect to OH

–

are the two

main parameters taken into consideration.

In theory, the transient state is assumed to take place at times short enough

to keep the concentration of (FeOH)

ads

“frozen” at its initial value. Therefore the

initial transition is due only to the change of the reaction rate of step (26) or (27)

under the effect of potential at constant (FeOH)

ads

concentration. The same

discrimination between instantaneous and delayed contributions is at the origin of

the frequency dependence of the faradic impedance. Table 1 shows the theoretical

and experimental values of the steady-state and transient kinetic parameters for

both mechanisms, according to Ref. 12.

According to Table 1, the delimitation between the two mechanisms relies on

a quite clear-cut difference in the set of kinetics criteria and would not involve

controversy at all. In fact, a careful analysis of literature data putting the emphasis

on experimental conditions leads to the following remarks [61,62]:

Tafel slope values are spread over a wide range from less than 30mV to more than

100 mV depending on ill-identified parameters. The role of metallurgical

factors such as dislocations and subgrain boundaries was interpreted as

favoring the catalytic mechanism (30 mV), whereas annealed iron with a low

density of structural defects would obey the consecutive mechanism (40 mV)

[61,62].

In many early studies iron dissolution was investigated as part of corrosion and

inhibition at open-circuit potential under an H

-saturated atmosphere, no

account being taken of the interference of the H

reaction with the Tafel

slopes [63,64]. Even under an inert atmosphere, the anodic parameters may be

affected by slow hysteresis phenomena resulting in steeper Tafel lines [65–69].

Reaction order measurements are not always very reliable and are sometimes

reported with fractional values [12].

Current transients are much too long to be consistent with the minimal exchange

current density still compatible with reaction (23) being at pseudoequilibrium

[70]. Alternative explanations based on local increase of pH have been

proposed [65] and further elaborated [70].

From the impedance approach it was then established that the iron mechanism

is far more complex than expected from early experiments and can hardly be

investigated correctly by current-voltage plots in spite of continued efforts

[71,72]. Thorough analysis over extended ranges of electrode potential, pH, and

frequency is presented in the following.

Atomistic Interpretation of the Catalytic Mechanism Anodic dissolution of

iron is probably the sole case for which an atomistic description was elaborated

with a somehow successful issue. An early attempt to explain the transient regime

of iron dissolution by relaxation of etched pits by a nucleation and growth model

can be found in Ref. 65 and is analyzed in Ref. 60. Starting in the middle of the

1970s, Heusler et al. have developed in a series of papers [29–31] an experimental

and modeling approach aimed at giving a crystallographic basis to the catalytic

mechanism. Correlation of kinetic and morphological data was performed on a

Anodic Dissolution 113

Table 1 Kinetic Data for Iron Dissolution at T = 298 K

Source: Ref. 12.

surface vicinal to {211} (misorientation ≅ 1°) of iron single crystals in acidic

solutions. These surfaces are found to develop a relatively simple steady-state

morphology made of triangular pyramids limited by nearly perfect {211} planes

and 〈311〉 edges. A schematic model of steps and kinks projected on a {111} plane

is given in Figure 3.

Steps are generated at the pyramid apex and move away on the three {211}

planes. The structure of the dissolving surface is determined by x

, the mean distance

of steps perpendicular to the 〈311〉 direction:

= bN

with b = interatomic distance

= probability of generation of six steps at the apex

= probability of kink generation at the intersection of two monatomic steps

and x

, the mean distance of kinks:

= bN

/ N

where N

is the probability of removing an atom from a kink.

The current density j is the product of the current on one kink ze

by the

density of kinks: j = ze

/ x

Scanning electron microscopy (SEM) examinations, [29] of the macroscopic

morphology of dissolution were then substantiated by transmission electron

microscopy (TEM) pictures of gold-decorated surfaces [30]. The better resolution,

even though not truly atomic, allowed an estimate of x

and x

and of their

dependence on the dissolution rate as shown in Figure 4. The surface concentration

of kinks (x

)

–1

is an exponential function of the potential with an exp(FE/RT)

114 Keddam

Figure 3. Schematic model of steps and kinks on crystallographic (211), (112) and (121)

planes projected into a (111) plane. From ref [30].

dependence. The potential-dependent parameter is x

≅ exp – (FE/RT) while the

mean distance of steps, x

, remains constant. Consistent with the catalytic

mechanism, at steady state the dissolution rate of atoms at kinks obeys an

exp(l + 2α)FE/RT Tafel law and, at constant kink density, the elementary rate of

atom dissolution is proportional to exp(RE/RT), i.e., α = 0.5 and transfer of n = 2

electrons in a single step.

Anodic Dissolution 115

Figure 4. Potential dependence of structural parameters and mean rates of elementary

processes for three different polarization conditions. TEM measurements on replica of

gold-decorated surfaces after anodic dissolution. Johnson-Matthey iron. From ref [30].